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Foundations Naive Set Theory by Halmos

  1. Strongly Recommend

  2. Lightly Recommend

  3. Lightly don't Recommend

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  4. Strongly don't Recommend

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  1. Mar 16, 2013 #1
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Mar 17, 2013 #2
    I skimmed this book while reading the opening chapter in the book Topology by James Munkres. The writting style of Paul Halmos is superb. There are not many problems designated as exercises; however, as I believe the author points out, the entire book is essentially an exercise. Hence, you will have plenty to do (verifying claims, filling in details, etc.)

    There are really no downsides to this text. Like I mentioned earlier, I used this book as a light supplement. But, I will say that carefully working through the opening chapter in Munkres provides a very solid foundation. I really did not need this book, but it did certainly have a refreshing style!
  4. Mar 17, 2013 #3


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    I guess one downside is that it doesn't develop set theory using ZFC IIRC.
  5. Mar 17, 2013 #4
    WannabeNewton, yes, you are right! I should have said that there are no downsides to the book when used as a supplement. For those interested diving deep into Set Theory (and perhaps never surfacing), Jech's tome would certainly be one route to take. =)
  6. Mar 17, 2013 #5


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    Warning: when he says you will never resurface, he isn't kidding.
  7. Mar 19, 2013 #6


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    Naive set theory is a book I read as a very young student, maybe in high school. You read it once, it gives you the universal language of mathematics and you never need to consult it again. I recommend it to anyone to learn the basic language of the subject. Nothing deep here, but everything is useful.
  8. Mar 26, 2015 #7
    This remains one of my favourite math texts. It gives you the language of sets and relations, functions and cartesian products, equivalence classes and 'the axiom of choice', plus a little more advanced set theory, in an easily digested format. You'll also understand Russell's paradox in a new way.

    Besides Halmos is a sublime communicator - one of the best in the business. You can pick up reprints up for $10-$15, and they're worth it purely for the example of crystal clear mathematical communication.
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